DOI10.1112/S0010437X06002521zbMath1127.16023arXivmath/0602259WikidataQ105615686 ScholiaQ105615686MaRDI QIDQ3434257
Fomin, Sergey, Andrei V. Zelevinsky
Publication date: 24 April 2007
Published in: Compositio Mathematica (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/math/0602259
The q-characters of minimal affinizations of type G2 arising from cluster algebras,
Exchange graphs for mutation-finite non-integer quivers,
Positive cluster complexes and τ-tilting simplicial complexes of cluster-tilted algebras of finite type,
Mixed dimer configuration model in type D cluster algebras,
Purity and Separation for Oriented Matroids,
Relative left Bongartz completions and their compatibility with mutations,
A CATEGORIFICATION OF ACYCLIC PRINCIPAL COEFFICIENT CLUSTER ALGEBRAS,
Dominance regions for rank two cluster algebras,
Dyck path categories and its relationships with cluster algebras,
Cluster scattering diagrams and theta functions for reciprocal generalized cluster algebras,
Associahedra for finite‐type cluster algebras and minimal relations between g‐vectors,
Reduction cohomology of Riemann surfaces,
Exchange graphs of cluster algebras have the non‐leaving‐face property,
Deformations of cluster mutations and invariant presymplectic forms,
Acyclic cluster algebras with dense \(g\)-vector fans,
Cluster duality between Calkin-Wilf tree and Stern-Brocot tree,
Perfect bases in representation theory: three mountains and their springs,
DILOGARITHM IDENTITIES IN CLUSTER SCATTERING DIAGRAMS,
On the mutation loops of valued quivers,
Tropical F$F$‐polynomials and general presentations,
Indices and \(c\)-vectors in extriangulated categories,
Celebrating Loday's associahedron,
Tetrahedron equation and quantum cluster algebras,
Quantization of deformed cluster Poisson varieties,
Gentle algebras arising from surfaces with orbifold points of order 3. I: Scattering diagrams,
On the properties of acyclic sign-skew-symmetric cluster algebras,
Quivers with potentials for Grassmannian cluster algebras,
Categorification of sign-skew-symmetric cluster algebras and some conjectures on \(\mathbf{g}\)-vectors,
Labelled seeds and the mutation group,
Adjacency for scattering amplitudes from the Gröbner fan,
The valuation pairing on an upper cluster algebra,
Homological approximations in persistence theory,
Denominator vectors and dimension vectors from triangulated surfaces,
Generalization of Markov Diophantine equation via generalized cluster algebra,
Infinitesimal semi‐invariant pictures and co‐amalgamation,
ABHY Associahedra and Newton polytopes of F$F$‐polynomials for cluster algebras of simply laced finite type,
Number of triangulations of a Möbius strip,
Unnamed Item,
Cluster algebras and symmetrizable matrices,
CLUSTER ALGEBRA AND COMPLEX VOLUME OF ONCE-PUNCTURED TORUS BUNDLES AND 2-BRIDGE LINKS,
-tilting theory,
-DEFORMED RATIONALS AND -CONTINUED FRACTIONS,
Linearity of stability conditions,
Compare triangular bases of acyclic quantum cluster algebras,
Affine cluster monomials are generalized minors,
Generators of rank 2 cluster algebras of affine types via linearization of seed mutations,
Cluster Algebras from Surfaces,
Cluster Characters,
Laurent phenomenon and simple modules of quiver Hecke algebras,
Cluster algebras and symmetric matrices,
Denominator vectors and compatibility degrees in cluster algebras of finite type,
Hankel Determinant Solutions to Several Discrete Integrable Systems and the Laurent Property,
Acyclic Cluster Algebras Revisited,
CONTINUOUS QUIVERS OF TYPE A (III) EMBEDDINGS OF CLUSTER THEORIES,
A 𝜏-tilting approach to the first Brauer-Thrall conjecture,
Dominance phenomena: mutation, scattering and cluster algebras,
The SAGEX review on scattering amplitudes Chapter 5: Analytic bootstraps for scattering amplitudes and beyond,
Classification of graded cluster algebras generated by rank 3 quivers,
Strongly primitive species with potentials. I: Mutations,
Cluster characters and the combinatorics of Toda systems,
Towards \(\mathcal{R}\)-matrix construction of Khovanov-Rozansky polynomials I. Primary \(T\)-deformation of HOMFLY,
Line defects, tropicalization, and multi-centered quiver quantum mechanics,
Cluster algebras and the positive Grassmannian,
Integrability as duality: the gauge/YBE correspondence,
Singularities of eight- and nine-particle amplitudes from cluster algebras and tropical geometry,
Unfolding of sign-skew-symmetric cluster algebras and its applications to positivity and \(F\)-polynomials,
The no gap conjecture for tame hereditary algebras,
On rooted cluster morphisms and cluster structures in 2-Calabi-Yau triangulated categories,
Cluster algebras, invariant theory, and Kronecker coefficients. II.,
Representations of \(U_q(L\mathfrak{sl}_2)\) at roots of unity and generalised cluster algebras,
On a family of Caldero-Chapoton algebras that have the Laurent phenomenon,
On Landau-Ginzburg models for quadrics and flat sections of Dubrovin connections,
Integrable cluster dynamics of directed networks and pentagram maps,
Symplectic double for moduli spaces of \(G\)-local systems on surfaces,
Tensor diagrams and cluster algebras,
Lower bound cluster algebras: presentations, Cohen-Macaulayness, and normality,
Theta series, wall-crossing and quantum dilogarithm identities,
Cluster categories for algebras of global dimension 2 and quivers with potential.,
\(F\)-polynomial formula from continued fractions,
Toda systems, cluster characters, and spectral networks,
Cluster automorphism groups of cluster algebras with coefficients,
Rigid and Schurian modules over cluster-tilted algebras of tame type,
Cluster structure on generalized Weyl algebras,
Polyhedral models for generalized associahedra via Coxeter elements,
On singularity confinement for the pentagram map,
Positivity for cluster algebras of rank 3,
Some conjectures on generalized cluster algebras via the cluster formula and \(D\)-matrix pattern,
Integrability of higher pentagram maps,
Cluster expansion formulas and perfect matchings,
Permutahedra and generalized associahedra.,
Initial-seed recursions and dualities for \(d\)-vectors,
On a category of cluster algebras,
Mutation classes of finite type cluster algebras with principal coefficients,
Discrete integrable systems and Poisson algebras from cluster maps,
Minkowski decomposition of associahedra and related combinatorics,
Cluster structures in 2-Calabi-Yau triangulated categories of Dynkin type with maximal rigid objects,
Diagrammatic description of \(c\)-vectors and \(d\)-vectors of cluster algebras of finite type,
Introducing supersymmetric frieze patterns and linear difference operators,
Cluster automorphism groups of cluster algebras of finite type,
A conjecture based on Somos-4 sequence and its extension,
Quiver Grassmannians associated with string modules.,
Quantum unipotent subgroup and dual canonical basis,
Donaldson-Thomas transformations of moduli spaces of G-local systems,
Maximum antichains in posets of quiver representations,
A Cambrian framework for the oriented cycle,
Kac-Moody groups and cluster algebras,
Polytopal realizations of finite type \(\mathbf{g}\)-vector fans,
The solution of the quantum \(A_1\) \(T\)-system for arbitrary boundary,
Rogers dilogarithms of higher degree and generalized cluster algebras,
A graph theoretic expansion formula for cluster algebras of classical type,
The devron property,
On sign-coherence of \(c\)-vectors,
Combinatorial expressions for \(F\)-polynomials in classical types,
Geometric realizations of the accordion complex of a dissection,
On the cluster nature and quantization of geometric \(R\)-matrices,
\(R\)-systems,
On Arnold's 14 `exceptional' \( \mathcal{N} = 2 \) superconformal gauge theories,
Laminations from the symplectic double,
Snake graph calculus and cluster algebras from surfaces. II: Self-crossing snake graphs,
Braids, complex volume and cluster algebras,
Cluster algebras from dualities of 2d \({\mathcal{N}} = (2, 2)\) quiver gauge theories,
Semi-invariant pictures and two conjectures on maximal green sequences,
\(c\)-vectors via \(\tau\)-tilting theory,
The greedy basis equals the theta basis: A rank two haiku,
Cluster algebras of type \(D_4\), tropical planes, and the positive tropical Grassmannian,
Cluster characters for 2-Calabi-Yau triangulated categories.,
Cluster algebras, invariant theory, and Kronecker coefficients. I,
Cluster algebras and semi-invariant rings. II: Projections,
Extensions in Jacobian algebras and cluster categories of marked surfaces,
On cluster algebras arising from unpunctured surfaces. II,
Examples of quantum cluster algebras associated to partial flag varieties.,
Quiver varieties and cluster algebras,
Cluster characters for cluster categories with infinite-dimensional morphism spaces,
The pentagram map and \(Y\)-patterns,
Denominators in cluster algebras of affine type.,
Discrete integrable systems, positivity, and continued fraction rearrangements,
Positivity for cluster algebras from surfaces,
Cluster algebras and Grassmannians of type \(G _{2}\),
Quantized Chebyshev polynomials and cluster characters with coefficients,
2-frieze patterns and the cluster structure of the space of polygons,
Cluster algebras and triangulated orbifolds,
Cluster algebras and quantum affine algebras,
Exchange relations for finite type cluster algebras with acyclic initial seed and principal coefficients,
Quasi-homomorphisms of cluster algebras,
Cluster algebras and triangulated surfaces. I: Cluster complexes,
Line defects and (framed) BPS quivers,
The quantum dilogarithm and representations of quantum cluster varieties,
Unistructurality of cluster algebras of type \(\widetilde{\mathbb{A}}\),
In memoriam: Andrei Zelevinsky (1953--2013),
Cambrian fans.,
Embeddings of root systems. II: Permutation root systems.,
Cluster algebras of finite type via Coxeter elements and principal minors.,
\(F\)-polynomials in quantum cluster algebras.,
Categorification of skew-symmetrizable cluster algebras,
Periodicity of Y-systems and flat connections,
\(Q\)-systems as cluster algebras. II: Cartan matrix of finite type and the polynomial property,
Tropical Grassmannians, cluster algebras and scattering amplitudes,
The enough \(g\)-pairs property and denominator vectors of cluster algebras,
Combinatorics of the \(q\)-characters of Hernandez-Leclerc modules,
Rationality of rigid quiver Grassmannians,
On folded cluster patterns of affine type,
Frieze varieties: a characterization of the finite-tame-wild trichotomy for acyclic quivers,
Exponents associated with \(Y\)-systems and their relationship with \(q\)-series,
Euler characteristics of quiver Grassmannians and Ringel-Hall algebras of string algebras.,
Cluster algebras of type \(A\) \(_{{2}}^{{(1)}}\),
An affine almost positive roots model,
Dominance order and monoidal categorification of cluster algebras,
Polyhedral parametrizations of canonical bases \& cluster duality,
On cluster variables of rank two acyclic cluster algebras,
Symplectic groupoids for cluster manifolds,
A combinatorial approach to scattering diagrams,
A combinatorial formula for rank 2 cluster variables,
Graded cluster algebras arising from marked surfaces,
Donaldson-Thomas invariants from tropical disks,
Non-commutative integrability of the Grassmann pentagram map,
The periodicity conjecture for pairs of Dynkin diagrams,
On type cones of \(g\)-vector fans,
Vector-relation configurations and plabic graphs,
Periodicities of T-systems and Y-systems, dilogarithm identities, and cluster algebras. I: Type \(B_r\),
Periodicities of T-systems and Y-systems, dilogarithm identities, and cluster algebras. II: Types \(C_r, F_4\), and \(G_2\),
Cluster algebras in algebraic Lie theory,
Acyclic quantum cluster algebras via Hall algebras of morphisms,
Quantum affine algebras and Grassmannians,
Cluster automorphism groups and automorphism groups of exchange graphs,
\(\mathcal{G}\)-systems,
An analog of Leclerc's conjecture for bases of quantum cluster algebras,
Newton polytopes of rank 3 cluster variables,
Phase constants in the Fock-Goncharov quantum cluster varieties,
Snake graphs from triangulated orbifolds,
Cluster realization of Weyl groups and \(q\)-characters of quantum affine algebras,
An introduction to supersymmetric cluster algebras,
Algebraic entropy of sign-stable mutation loops,
Universal quivers,
Relation between \(f\)-vectors and \(d\)-vectors in cluster algebras of finite type or rank 2,
Algebraic branch points at all loop orders from positive kinematics and wall crossing,
Cluster-enriched Yang-Baxter equation from SUSY gauge theories,
Universal geometric coefficients for the four-punctured sphere,
Presentations of cluster modular groups and generation by cluster Dehn twists,
Cluster integrable systems, \(q\)-Painlevé equations and their quantization,
Families of Gröbner degenerations, Grassmannians and universal cluster algebras,
Universal geometric cluster algebras,
Graded quiver varieties, quantum cluster algebras and dual canonical basis,
\(\tau^2\)-stable tilting complexes over weighted projective lines,
Arithmetics of 2-friezes,
More Arnold's \( \mathcal{N} = 2 \) superconformal gauge theories,
Wall-crossing, Rogers dilogarithm, and the QK/HK correspondence,
On the structure of quadrilateral brane tilings,
Quiver mutation loops and partition \(q\)-series,
Donaldson-Thomas transformation of Grassmannian,
On some combinatorial properties of generalized cluster algebras,
MHV amplitudes at strong coupling and linearized TBA equations,
Uniform column sign-coherence and the existence of maximal green sequences,
Non-perturbative geometries for planar \(\mathcal{N} = 4\) SYM amplitudes,
Symplectic frieze patterns,
Cluster integrable systems and spin chains,
Algebraic singularities of scattering amplitudes from tropical geometry,
A conjecture on cluster automorphisms of cluster algebras,
\(c\)-vectors of 2-Calabi-Yau categories and Borel subalgebras of \(\mathfrak{sl}_\infty \),
Positivity of denominator vectors of skew-symmetric cluster algebras,
Cluster realizations of Weyl groups and higher Teichmüller theory,
Colored BPS pyramid partition functions, quivers and cluster transformations,
Towards a uniform subword complex description of acyclic finite type cluster algebras,
BPS quivers of five-dimensional SCFTs, topological strings and \(q\)-Painlevé equations,
A quantum cluster algebra approach to representations of simply laced quantum affine algebras,
Notes on cluster algebras and some all-loop Feynman integrals,
Difference equations arising from cluster algebras,
Cluster variables, ancestral triangles and Alexander polynomials,
Combinatorics of canonical bases revisited: type A,
One-loop integrand from generalised scattering equations,
Some consequences of categorification,
An expansion formula for type \(A\) and Kronecker quantum cluster algebras,
Jacobian matrices of Y-seed mutations,
Newton-Okounkov bodies, cluster duality, and mirror symmetry for Grassmannians,
Plabic \(R\)-matrices,
Cluster structures and subfans in scattering diagrams,
An expansion formula for quantum cluster algebras from unpunctured triangulated surfaces,
Infinite rank surface cluster algebras,
Minkowski decompositions for generalized associahedra of acyclic type,
Horizontal and vertical mutation fans,
Cluster Toda chains and Nekrasov functions,
Wall and chamber structure for finite-dimensional algebras,
Cluster algebras and Jones polynomials,
A proof of Lee-Lee's conjecture about geometry of rigid modules,
Cluster automorphisms and quasi-automorphisms,
Maximal Green sequences for cluster-tilted algebras of finite representation type,
Tropical fans, scattering equations and amplitudes,
Redundancy in string cone inequalities and multiplicities in potential functions on cluster varieties,
\( \tilde{A}\) and \(\tilde{D}\) type cluster algebras: triangulated surfaces and friezes,
Symbol alphabets from tensor diagrams,
Truncated cluster algebras and Feynman integrals with algebraic letters,
Duality between final-seed and initial-seed mutations in cluster algebras,
Factoriality and class groups of cluster algebras,
Categorified canonical bases and framed BPS states,
Quantum cluster characters of Hall algebras revisited,
Torsion functions on moduli spaces in view of the cluster algebra,
Equivariant multiplicities via representations of quantum affine algebras,
Integrable clusters,
Quantization of canonical bases and the quantum symplectic double,
Saturation of Newton polytopes of type A and D cluster variables,
Solutions to the T-systems with principal coefficients,
The existence of a maximal Green sequence is not invariant under quiver mutation,
Diophantine equations via cluster transformations,
Quantum cluster variables via Serre polynomials,
Donaldson-Thomas theory and cluster algebras,
Universal associahedra,
Combinatorics of \(\mathcal X\)-variables in finite type cluster algebras,
Cluster fan of \(\mathbf z\)-vectors and toric degenerations,
A 2-Calabi-Yau realization of finite-type cluster algebras with universal coefficients,
Twists of Plücker coordinates as dimer partition functions,
POSITIVITY FOR REGULAR CLUSTER CHARACTERS IN ACYCLIC CLUSTER ALGEBRAS,
Newton–Okounkov Bodies of Flag Varieties and Combinatorial Mutations,
CLUSTER AUTOMORPHISMS AND COMPATIBILITY OF CLUSTER VARIABLES,
Growth rate of cluster algebras,
m-Noncrossing trees,
Compatibility fans for graphical nested complexes,
Universal geometric cluster algebras from surfaces,
Bases for cluster algebras from orbifolds,
\(F\)-matrices of cluster algebras from triangulated surfaces,
Cluster algebras arising from cluster tubes I: integer vectors,
Cluster configuration spaces of finite type,
Modular Fuss-Catalan numbers,
Quantum cluster characters for valued quivers,
Minimal length maximal green sequences,
QRT maps and related Laurent systems,
Asymptotic Sign Coherence Conjecture,
Mixed cobinary trees,
Knot theory and cluster algebras,
Newton-Okounkov bodies for categories of modules over quiver Hecke algebras,
Schubert problems, positivity and symbol letters,
Combinatorial cluster expansion formulas from triangulated surfaces,
Geometric description of \(C\)-vectors and real Lösungen,
Bases for cluster algebras from orbifolds with one marked point,
Cluster scattering diagrams and theta basis for reciprocal generalized cluster algebras,
Unistructurality of cluster algebras,
Cambrian frameworks for cluster algebras of affine type,
Combinatorics of X-variables in finite type cluster algebras,
The action of a Coxeter element on an affine root system,
A CONJECTURE ON -MATRICES OF CLUSTER ALGEBRAS,
Webs on surfaces, rings of invariants, and clusters,
Cluster-like coordinates in supersymmetric quantum field theory,
Cluster algebras and continued fractions,
Some integrable maps and their Hirota bilinear forms,
Greedy elements in rank 2 cluster algebras,
Snake graph calculus and cluster algebras from surfaces,
Cluster ensembles and Kac-Moody groups,
Maximal green sequences of skew-symmetrizable \(3\times 3\) matrices,
A geometric q‐character formula for snake modules,
Cluster $\mathcal X$-varieties for dual Poisson–Lie groups. I,
QUANTISATION SPACES OF CLUSTER ALGEBRAS,
Toric degenerations of cluster varieties and cluster duality,
Periodicity, linearizability, and integrability in seed mutations of type AN(1),
Polylogarithm Identities, Cluster Algebras and the $$\mathcal {N} = 4$$ Supersymmetric Theory,
Sequences of reflection functors and the preprojective component of a valued quiver.,
Analytic solutions and integrability for bilinear recurrences of order six,
Periodicities of T-systems and Y-systems,
Cluster Structures on Double Bott–Samelson Cells,
Cluster Algebras and Triangulated Surfaces Part II: Lambda Lengths,
From the Tamari Lattice to Cambrian Lattices and Beyond,
Dilogarithm identities for conformal field theories and cluster algebras: Simply laced case,
Bases for cluster algebras from surfaces,
Quivers with potentials associated to triangulated surfaces, Part III: tagged triangulations and cluster monomials,
A Module-Theoretic Interpretation of Schiffler's Expansion Formula,
A Correspondence between Rigid Modules Over Path Algebras and Simple Curves on Riemann Surfaces,
Quivers with potentials and their representations II: Applications to cluster algebras,
Oriented Flip Graphs and Noncrossing Tree Partitions,
On cluster algebras with coefficients and 2-Calabi-Yau categories,
Polyhedral models for tensor product multiplicities,
Duality for discrete integrable systems II,
On cluster algebras from unpunctured surfaces with one marked point,
Wonder of sine-Gordon $Y$-systems,
ORIENTED FLIP GRAPHS, NONCROSSING TREE PARTITIONS, AND REPRESENTATION THEORY OF TILING ALGEBRAS,
ON THE NUMBER OF POINTS OVER FINITE FIELDS ON VARIETIES RELATED TO CLUSTER ALGEBRAS,
Unistructurality of cluster algebras from unpunctured surfaces,
Comments on Exchange Graphs in Cluster Algebras,
Powers of Coxeter elements in infinite groups are reduced,
Y-meshes and generalized pentagram maps,
Quiver Grassmannians of Extended Dynkin type 𝐷 Part 1: Schubert Systems and Decompositions Into Affine Spaces,
Three lectures on quiver Grassmannians,
A survey on maximal green sequences,
Sortable elements in infinite Coxeter groups,
Cluster structures for 2-Calabi–Yau categories and unipotent groups,
Lifting to Cluster-Tilting Objects in 2-Calabi–Yau Triangulated Categories,
Maximal rigid objects without loops in connected 2-CY categories are cluster-tilting objects,
Cluster algebras via cluster categories with infinite-dimensional morphism spaces,
Quantum Grothendieck rings as quantum cluster algebras,
Monoidal Categorifications of Cluster Algebras of Type A and D,
Synchronicity phenomenon in cluster patterns,
Generic bases for cluster algebras and the Chamber Ansatz,
FRIEZES, STRINGS AND CLUSTER VARIABLES,
LINEAR RELATIONS AND INTEGRABILITY FOR CLUSTER ALGEBRAS FROM AFFINE QUIVERS,
Lifting to Cluster-tilting Objects in Higher Cluster Categories,
Linear independence of cluster monomials for skew-symmetric cluster algebras,
Canonical bases for cluster algebras,
Modules Over Cluster-Tilted Algebras Determined by Their Dimension Vectors,
Cluster algebras: an introduction,
On Jacobian algebras associated with the once-punctured torus,
Positivity for cluster algebras,
Quantum dilogarithms and partition \(q\)-series